Ans: (a) $x>\dfrac{25}{4}$ (b) $7$, $8$ and $9$
-
$\begin{array}{rcl}
\dfrac{19-7x}{3} & > & 23-5x \\
19-7x & > & 69 – 15x \\
8x & > & 50 \\
x & > & \dfrac{25}{4}
\end{array}$ -
$\begin{array}{rcl}
18-2x & \ge & 0 \\
-2x & \ge & -18 \\
x & \le & 9
\end{array}$Therefore, the overall solutions of the compounded inequality are $\dfrac{25}{4} < x \le 9$. Hence, the integers satisfying the inequalities are $7$, $8$ and $9$.
